56 | P a g e

Linear Motion Unit Student Design Cover Page(see guidelines on page 19)

57 | P a g e

Linear Motion Unit Front Page

At the end of this unit, I will:

Roots, Prefixes, and Suffixes I will understand and recognize are: Linear Motion: per, de-,

The terms I will clearly define are: Linear Motion: rate, speed, velocity, instantaneous speed, average speed, acceleration,

free fall, deceleration Vectors: vector, scalar, resultant

The assignments I will have completed by the end of this unit are:q Intro to Linear Motion Notes (Pg. 59)q Intro to Vectors Notes (Pg. 61)q Intro to Vectors Practice (Pg. 60)q Vector Math Practice (Pg. 62)q Jumping Frog Lab (Pg. 64-67)q Acceleration Notes (Pg. 68)q Review Questions (Pg. 68)q Using Equations Practice (Pg. 57)q Acceleration, Distance, Velocity Equations (Pg. 72)q Reaction Rate Lab (Pg. 74 - 77)q Graphing Motion Notes (Pg. 78 - 79)q Motion Graphs Practice (Pg. 80 - 81)q Motion Problems Guided Practice (Pg. 84 - 8585)q Linear Motion Practice Problems (Pg. 85 - 88)q Plug & Chug Problems (Pg. 89 - 90)q Using KUES to Solve Problems (Pg. 82 - 83)q Distance vs. Displacement Notes & Practice (Pg. 91 - 92)q Linear Motion Study Guide (Pg. 93 - 96)q Concept Cards (Pg. 97)q Concept Map (Pg. 98)q Unit Back Page (Pg. 99)

58 | P a g e

Intro to Linear Motion Notes

What is a rate?A rate tells us __________________________________________________________________________________________________________________________________________For example: ______________________________________________________________

What is speed?Speed is a measure of how fast something is _________________________. It is the rate at which _______________________________ is covered.

What are some examples of units for speed?

What is the difference between instantaneous and average speed?

Instantaneous speed is the speed ____________________________________________________________________________________________________________________For example: ______________________________________________________________

Average speed does not indicate variations in the speed that may take place during a trip. Instead, it is the total ________________________________________________ divided by the ___________________________________.

What is the “formula” for calculating average speed?

What is the difference between speed and velocity?

Velocity is _______________________________________________________________.

What is constant velocity?

_________________________________________ is when both the ________________________ and __________________________ are constant.

What is changing velocity?

If _________________________ the speed or the direction (or both) are changing, then the _____________________________ is changing.

Summary:

59 | P a g e

Intro Vectors Practice

1. Which of the following is a scalar quantity? (circle all)a. A weight of 50 Nb. 20 seconds of timec. a mass of 10 kgd. the length of your pencile. instructions on a treasure mapf. the force of frictiong. your ageh. 5 m/s, West

2. Find the resultant of 55.4 units W and 69.2 units S.

3. What is the resultant of 1,230 m/s, S and 1,450 m/s, N?

4. If you walk 6.00 m, N and 5.00 m E, what is your final location from your start(in other words, what is your resultant)?

5. Combine 27 mi/h, E and 73 mi/h, N.

60 | P a g e

Remember:A2 + B2 = C2

Intro to Vectors Notes

Why do we need to use vectors in physics?

Remember that velocity is both speed and ________________________________

Vectors are ways to represent both __________________________ and _________________________________________.

What is the difference between a vector quantity and a scalar quantity?

Vector quantities have ______________________________________________________________________________________________________________________________________Example: _____________________________________________________________________

Scalar quantities have _______________________________________________________Example: _____________________________________________________________________

How are vectors usually represented?

Vectors are usually drawn as an ____________________________________________

Draw a vector with a large magnitude and a direction of south.

Draw a vector with a small magnitude and a negative direction.

What is a resultant?A resultant is the sum of adding _______________________________________It is calculated using the following formula:

Draw a resultant for two perpendicular vectors and calculate its magnitude.

Summary:

61 | P a g e

Vector Math Practice

1. A river flows at a speed of 12 m/s from north to south. A powerboat can move at a constant maximum speed of 23 m/s in still water.

a. Draw this scenario below:

b. What is the maximum velocity of the boat upstream (upstream means traveling against the current)? ____________

c. What is the maximum velocity of the boat downstream? __________d. Use vectors to draw what would happen if the boat were headed east across the

river at its maximum speed.

e. What would the resultant velocity of the boat be now?

2. A plane is travelling toward the east with a velocity of 120 km/h. It encounters a wind blowing toward the east at 0.20 km/min. (be careful with units!)

a. Draw this scenario below:

b. What is the velocity of the plane in km/h?

3. A pitcher can throw a ball at a velocity of 125 km/h straight ahead. a. Draw vectors to represent what would happen if he threw the ball straight when

a cross-wind is blowing at 28 km/h to the left.

b. What will be the magnitude of the ball's resultant velocity?

62 | P a g e

63 | P a g e

How to Make a Jumping Frog

64 | P a g e

65 | P a g e

Frog Race Activity Abstract

Frog Race Activity Data & Calculations

My fastest time:

Winner for my group: (with a time of )

My track length:

Name of winner Distance Time

66 | P a g e

Frog Race Activity Procedure & Questions

Procedure:

1. Practice making your frog jump by pushing gently on its back. 2. Start the frog at the starting line, marked at one end of the table, and have a partner use

a stopwatch to measure the time it takes the frog to cross the finish line. 3. After 3 trials, record your fastest time, to the nearest 0.1 s, on the data sheet. 4. Repeat for everyone in your group. Record the “winner” with the fastest time on your

data sheet. 5. Measure the distance of the track your frog was on to the nearest 0.1 cm. Record it on

your data sheet.

Conclusion Questions:

1. Why was it unfair to declare a class champion based on times alone?

2. What should be compared to see which frog is actually the fastest?

3. Did you calculate the frog’s speed or velocity? Explain.

4. In this lab, explain why it was or was not necessary to calculate velocity.

67 | P a g e

Review Questions(refer to Chapter 2 in your textbook for more help!)

1. Does the speedometer of a car measure instantaneous speed or average speed?

2. If the speedometer of a car reads a constant speed of 40 km/hr, can you say the car has

a constant velocity? Why or why not?

3. What two parts of a car can change its speed?

What is the only part of a car that can change velocity but not speed?

4. What is the acceleration of a car that travels in a straight line and increases its speed from 0 to 100 km/hr in 10 seconds?

5. By how much does the speed of a vehicle that is travelling in a straight line change each second when it is accelerating at 2 km/ hs?

6. Calculate the average speed (in m/s) of a cheetah that runs 140 meters in 5 seconds.

7. Calculate the average speed (in km/hr) of Charlie, who runs to the store 4 km away in 30 minutes.

8. Calculate the acceleration of a car that can go from rest to 112 km/hr in 10 seconds.

68 | P a g e

Acceleration Notes

What is acceleration?Acceleration is the rate at which _______________________________________ is changing.

Write the general formula for acceleration.

What letter represents acceleration?

What is deceleration?

In physics, the term _______________________________________ applies to decreases as well as increases in speed. A decrease in speed is often called deceleration or ___________________________________________________Example: _________________________________________________________________

Is acceleration always speeding up or slowing down?

Acceleration applies to changes in _________________________ as well as changes in speed.

Example: ___________________________________________________________________Even if your ____________________________ is constant, if your direction is changing then your __________________________________________ is changing and thus it is considered acceleration.

What are the units for acceleration?

Acceleration is a change in velocity per time interval, and is measured in units such as:

What is freefall?Freely falling objects are _________________________________________________________________________________________________________________________________

What is the acceleration of an object due to gravity?

Summary:

69 | P a g e

70 | P a g e

∆d∆t

Using Equations Practice

1. Rearrange to solve for t :v = at

2. Rearrange to solve for v0:v = v0 + at

3. Rearrange to solve for ∆t:

v =

4. Rearrange to solve for t:

d = ½ at2

5. Fill in the table below:

Symbol Variable Units

a m/s2

m/s

distance/displacement

t

6. Explain how you calculate ∆ velocity and why ∆v is different than vf

71 | P a g e

∆d∆t

∆v∆t

Acceleration, Distance, Velocity Equations

A few symbols to know:

∆

V0

Vf

a

v

d

t

v =

a =

v = gt

v = at

72 | P a g e

d = ½ at2

73 | P a g e

Reaction Rate Lab – Flow Chart

74 | P a g e

Reaction Rate Lab – Data & Calculations

Part A Data:

Length of the dollar bill (in meters):

Length of half of the dollar bill (in meters):

Observations: Describe what happened. Were you able to catch the dollar bill?

Part B Data:

Trial # Reaction Distance (m)

1

2

3

Average

Part B Calculations:1. Which acceleration equation allows us to calculate “t” when we know “d” and “a”?

2. Rearrange this equation to solve for “t”.

3. Since the object is falling, “a” is equal to .

4. Use your average d and solve for your reaction time.

75 | P a g e

Reaction Rate Lab – Procedure

It takes a fraction of a second for brain impulses to travel from your eye to your brain and then to your fingers. Reaction times vary from person to person. In this lab, your task will be to determine your reaction time using only a meter stick and a small ruler (no clock or timer will be provided).

Problem: Can you catch a dollar bill that is dropped between your fingers?

Hypothesis: If a dollar bill is dropped between the subject’s fingers, then because

(In this lab, you are the “subject”!)

Part A – The bet1. Measure the length of the dollar bill in meters. Record in the data table on page 75

under “Part A”.2. Calculate the midpoint of the dollar bill and lightly mark it on the bill. 3. Hold the dollar bill so that the midpoint hangs between your partner’s thumb and

finger. 4. Drop the dollar bill and have your partner catch it on the way down only by closing the

fingers (not by moving the arm).5. Record your observations on the data and calculations sheet on page 75.

Part B – Determining reaction time1. Hold a meter stick between the thumb and forefinger of your lab partner. The thumb

and finger should be spread 5.0 cm apart to insure consistency. Make sure to check this distance, and don’t allow cheating!

2. Make the 50 cm mark on the meter stick even with your partner’s fingers. 3. Drop the meter stick and have your partner catch it on the way down only by closing the

fingers (not by moving the arm down). Do not announce when you are about to drop the meter stick.

4. Measure the distance the stick fell before it was caught. Record on the data table on page 75.

5. Repeat twice more and get an average distance.6. Swap places with your partner and repeat to find your own reaction distance.7. Complete the calculations under “Part B” on page 75.

76 | P a g e

Reaction Rate Lab – Conclusion Questions

Answer the questions below on this page. Show all of your work. You do not need to include the calculations for these questions in your lab report, but you do need to discuss the questions, their answers, and how this relate to the lab in your report.

1. The hand-eye reaction time for the average person is 0.15 sec. How far will any object fall in that time? Show your work.

2. Why would it be important to drop the bill vertically rather than at a slight angle?

3. Why was it necessary to record the distances in meters and not cm or mm?

4. What factors does this lab not take into consideration?

77 | P a g e

Graphing Motion Notes

Distance vs. Time Graph:

Velocity (or speed) vs. Time Graph:

78 | P a g e

Graphing Motion NotesWhat types of graphs do we use to study motion?

In our study of motions we will most frequently use graphs and graphs.

How is a distance vs. time graph plotted?

X axis:Y axis:

What do distance vs. time graphs show us?

A distance-time graph shows us

The steeper the graph, the the motion.

A horizontal line means the object is not changing its position( )

A downward sloping line means the object is

How is a velocity vs. time graph plotted?

X axis:Y axis:

What do velocity vs. time graphs show us?

A velocity-time graph shows us

The steeper the graph, the greater the

A means the object is moving at a steady speed.

A downward sloping line means the object is

Summary:

79 | P a g e

Motion Graphs Practice

Look at the graph to the right. It shows how three runners ran a 100-meter race.

1. Which runner won the race? How

do you know this?

2. Which runner stopped for a rest?

3. How long did he stop for?

4. How long did Bob take to complete the race?

5. Calculate Albert's average speed.

Acceleration is the rate at which velocity changes. Since velocity is both speed and direction, if speed changes, then velocity changes. The rate at which this happens is the object’s acceleration. The graph to the right shows how the speed of a bus changes during part of a journey

6. Label each segment of the journey with the correct number from the following list:

a. accelerating

b. decelerating

c. steady speed

d. stationary

7. During which part of the journey was the bus moving fastest?

8. During which part of the journey did the bus have greatest acceleration, either positive

or negative?

80 | P a g e

9. Calculate the acceleration between D and E.

Motion Graphs Practice

The graph on the right shows the motion of a moving car.

10. In which section is the car

accelerating from rest?

11. In which section is the car’s

acceleration negative?

12. How far does the car travel during

section “b”?

13. What is the acceleration of the car in section a?

The graph on the right shows distance and time for a moving cart.

14. In which section(s) is the cart

accelerating?

15. In which section(s) is the cart not

moving?

16. In which section(s) is the cart moving

backwards?

17. What is the velocity of the cart between

sections e-f?

18. How far does the cart move in section b-c?

81 | P a g e

Using KUES to Solve Problems

1. What is the velocity (in miles/hr) of a car traveling north on I-75 if it takes 2 hours to reach Chattanooga (120 miles)?

Known: Unknown: Equation(s):

Work:

Solution:

2. A car starts from rest and reaches a velocity of 22.0 m/s in 20.0 seconds. What is its acceleration?

Known: Unknown: Equation(s):

Work:

Solution:

82 | P a g e

Using KUES to Solve Problems

Physics problems must be solved completely using the scientific approach K-U-E-S.

Knowns – write the known values (include units) and its variable symbol.

Unknowns – write the variable symbol for what you will be solving for

Equation – write the equation you will be using (symbols only!)

Substitute & Solve - Substitute the known values (numbers & units) for the letters in the equation.

The answer should be circled/boxed and contain correct significant digits & units and no fractions.

First, we’ll try one together:

A. A bullet is fired at 660 m/s and strikes a target 200.0 meters away. What is the duration of the bullet’s flight?

Known: Unknown: Equation(s):

Work:

Solution:

83 | P a g e

Motion Problems Guided Practice

1. A boy sliding down a hill accelerates at 1.40 m/s2. If he started from rest, in what distance would he reach a velocity of 7.00 m/s?

2. Light travels in a straight line at a constant speed of 3.0 x 10 8 m/s for 4.1 years to reach the earth from the nearest star 3.9 x 10 13 km away. What is its acceleration?

3. If a bullet leaves the muzzle of a rifle with a speed of 600 m/s, and the barrel of the rifle is 0.9 m long, at what rate is the bullet accelerated while in the barrel?

4. A car is traveling at a velocity of 22 m/s when the driver puts on the brakes to decelerate it at 1.4 m/s2 over a distance of 110 m. What is the car’s velocity at the end of this distance?

5. A ball, originally at rest, undergoes a constant acceleration of 0.76m/s2. How long does it take the ball to travel 4.8m?

84 | P a g e

Motion Problems Guided Practice

A. A car with a velocity of 22 m/s is accelerated uniformly at the rate of 1.6 m/s2 for 6.8 s. What is its final velocity?

Known: Unknown: Equation(s):

Work:

Solution:

B. What is the acceleration of a plane that changes velocity from 75 m/s to 140 m/s in 15s? How far does a plane fly during that time?

Known: Unknown: Equation(s):

Work:

Solution:

85 | P a g e

86 | P a g e

Linear Motion Practice Problems

1. A student drops a rock from a bridge to the water 12 m below. a) How many seconds does it take the rock to hit the water?

b) How fast is the rock moving when it hits the water?

2. A weather balloon is floating at a certain height above the earth when it releases a heavy pack of instruments. a) If the pack hits the ground with a speed of 73 m/s, how far up is the balloon?

b) How long does it take the instrument pack to reach the ground?

3. An engineer must design a runway that allows planes to reach a ground speed of 61 m/s before they can take off. If the planes accelerate at 2.4 m/s2, what must be the minimum length of the runway?

4. A rock is thrown straight down, not dropped, from the roof of a building that is 61 m above the ground. If it takes 3.1 s to reach the ground, with what speed was it thrown?

87 | P a g e

Linear Motion Practice Problems

5. A baseball is hit straight up into the air with a speed of 33 m/s.a) How high does it go?

b) How long is it in the air?

6. An astronaut drops a feather from 1.25 m above the surface of the moon. The acceleration due to gravity on the moon is 1.62 m/s2.a) How long does it take the feather to hit the ground?

b) How long would it take a hammer to fall the same distance?

7. A tennis ball is dropped 1.2 m above the ground. With what velocity does it hit the ground (before the ground stops it)?

88 | P a g e

Plug & Chug Problems

1. Calculate the average speed (in m/s) of a cheetah that runs 140 meters in 5 seconds.

2.a. Calculate the average speed (in km/hr) of Charlie, who runs to the store 4

kilometers away in 30 minutes.

b. Calculate the distance that Charlie runs if the maintains this average speed for 1 hour.

3. Calculate the acceleration of a car (in km/hs) that can go from rest to 100 km/hr in 10s.

4. Calculate the instantaneous speed (in m/s) at the 10 second mark for a car that accelerates at 2 m/s2 from a position of rest.

89 | P a g e

Plug & Chug Problems

5. Calculate the speed (in m/s) of a skateboarder who accelerates from rest for 3 seconds down a ramp at an acceleration of 5 m/s2.

6. Calculate the instantaneous speed of an apple that falls freely from a rest position and accelerates at 10 m/s2 for 1.5 seconds.

7. An object is dropped from rest and falls freely. After 6 seconds, calculate its instantaneous speed, average speed, and distance fallen.

8. Calculate the instantaneous speed and distance fallen for an object that falls freely from rest for 8 seconds.

90 | P a g e

Distance vs. Displacement Practice

Calculate the distance and displacement in each of the following situations. Include a direction (example: north or northwest) with your answer.

1. Alex walks east for 3 km, stops for a break, and then runs the same direction for 4 km before he stops.

2. David walks 3 km north, and then turns east and walks 4 km.

3. Amy runs 2 miles south, then turns around and runs 3 miles north.

4. Jermaine runs exactly 2 laps around a 400 meter track.

5. Derrick crawls 4 feet south, and then turns east and crawls 6 feet.

6. Ray runs 30 feet north, 30 feet west, and then 30 feet south.

7. Cassidee walks 1 mile north then turns west and walks 2 miles.

8. Taja walks two miles north from her door to the park, then returns home to her door.

9. Sandy ran 8 blocks north, and then 2 blocks south back toward her starting point.

10. Neva swam 3 complete laps in a 50 meter pool. (1 lap is one length of the pool)

91 | P a g e

Remember:A2 + B2 = C2

Distance vs. Displacement Notes

What is distance?

Distance refers to _________________________________________________________ ________________________________________________________during its motion.

It is the total distance travelled or the total distance an object has moved.

Is distance a scalar or vector quantity?

What is displacement?

Displacement refers to ______________________________________________________________________ an object is.

It is the object's overall change in position.

Is displacement a vector or scalar quantity?

Example #1:

What is the displacement of the cross-country team if they begin at the school, run 10 miles and finish back at the school?

Example #2:

What is the distance and the displacement of the race car drivers in the Indy 500?

SUMMARY:

92 | P a g e

Linear Motion Study Guide

Part 1: Reviewq Look through all of the pages in this unit. Is there anything you did not complete? Finish

it now as extra practice for the test. q Look back over your Cornell notes for this unit. Cover the right half of the page and see if

you can answer the questions on the left. Study any information you cannot answer without peeking at the right side.

q Use your concept cards to study key terms. q Practice rearranging the equations we used this unit. Determine the most important

ones and include them on your “cheat sheet”.q Read the summaries you wrote for each set of notes. Underline important or key terms.

Part 2: Practice1. What is the difference between speed and velocity?

2. Mark the following as vector or scalar quantities:a. 18 kg ______________________b. 35 degrees SW __________________________c. 59 seconds ______________________d. 15 mph north ____________________________e. 32 meters ___________________________

3. What is the difference between distance and displacement?

4. What is the difference between average and instantaneous speed?

5. A car driving in a circle at 40 mi/h does not change (speed or velocity) but does change (speed or velocity).

6. The rate of change in velocity is called _________________________________________________.

7. Acceleration due to gravity, represented by the letter ______ is about _____________ in most of the USA.

8. If an object has uniform or constant velocity, its acceleration = _________.

93 | P a g e

Linear Motion Study Guide

9. True or false? If an object undergoes even acceleration, its velocity does not change.

10. Draw a picture of a hill down which a ball would roll with:a. increasing “v” and decreasing “a”

b. increasing “v” and constant “a”

c. increasing “v” and increasing “a”

Use the graphs above to answer the questions below.

11. Which graph shows uniform motion? 12. Which graph shows acceleration?

13. The Road Runner steps off a ledge and drops to the ground in 0.50 s. What is Road Runner's velocity the instant it hits? How high is the ledge off the ground?

94 | P a g e

Linear Motion Study Guide

14. In 2.8 s, a car increases its velocity from 20. m/s to 25 m/s. What is the acceleration of the car?

15. How long will it take to stop a car if its driver starts braking at a velocity of 32m/s and decelerates the car at 5.0 m/s2? How far will the car travel before it stops?

95 | P a g e

Linear Motion Study Guide

16. A man is driving a car at a constant velocity of 55 mi/h. If he looks down at the radio for 2.2 s, how far has the car moved?

17. In a test of car bumpers, a car moving 7.0 m/s collides head-on with a wall. From what height would the car have to be dropped in order to collide with the ground at the same velocity?

96 | P a g e

Linear Motion Unit Concept Cards(see page 13-14 for directions)

97 | P a g e

Linear Motion Unit Concept Map(See page 19 for directions)

98 | P a g e

Linear Motion Unit Back Page

The terms I can clearly define are:q accelerationq average speedq decelerationq displacementq distanceq free fallq instantaneous speedq rateq resultantq scalar quantity q speedq vector quantityq velocity

The California Dept. of Education Standards I have come to understand are:

(Physics)

q 1.A Students know how to solve problems that involve constant speed and average speed.

q 1. J. Students know how to resolve two-dimensional vectors into their components and calculate the magnitude and direction of a vector from its components.

99 | P a g e